Poster presentation: Functional connectivity of the brain describes the network of correlated activities of different brain areas. However, correlation does not imply causality and most synchronization measures do not distinguish causal and non-causal interactions among remote brain areas, i.e. determine the effective connectivity [1]. Identification of causal interactions in brain networks is fundamental to understanding the processing of information. Attempts at unveiling signs of functional or effective connectivity from non-invasive Magneto-/Electroencephalographic (M/EEG) recordings at the sensor level are hampered by volume conduction leading to correlated sensor signals without the presence of effective connectivity. Here, we make use of the transfer entropy (TE) concept to establish effective connectivity. The formalism of TE has been proposed as a rigorous quantification of the information flow among systems in interaction and is a natural generalization of mutual information [2]. In contrast to Granger causality, TE is a non-linear measure and not influenced by volume conduction. ...

Poster presentation: Twenty Second Annual Computational Neuroscience Meeting: CNS*2013. Paris, France. 13-18 July 2013.
When studying real world complex networks, one rarely has full access to all their components. As an example, the central nervous system of the human consists of 1011 neurons which are each connected to thousands of other neurons [1]. Of these 100 billion neurons, at most a few hundred can be recorded in parallel. Thus observations are hampered by immense subsampling. While subsampling does not affect the observables of single neuron activity, it can heavily distort observables which characterize interactions between pairs or groups of neurons [2]. Without a precise understanding how subsampling affects these observables, inference on neural network dynamics from subsampled neural data remains limited.
We systematically studied subsampling effects in three self-organized critical (SOC) models, since this class of models can reproduce the spatio-temporal activity of spontaneous activity observed in vivo [2,3]. The models differed in their topology and in their precise interaction rules. The first model consisted of locally connected integrate- and fire units, thereby resembling cortical activity propagation mechanisms [2]. The second model had the same interaction rules but random connectivity [4]. The third model had local connectivity but different activity propagation rules [5]. As a measure of network dynamics, we characterized the spatio-temporal waves of activity, called avalanches. Avalanches are characteristic for SOC models and neural tissue [6]. Avalanche measures A (e.g. size, duration, shape) were calculated for the fully sampled and the subsampled models. To mimic subsampling in the models, we considered the activity of a subset of units only, discarding the activity of all the other units.
Under subsampling the avalanche measures A depended on three main factors: First, A depended on the interaction rules of the model and its topology, thus each model showed its own characteristic subsampling effects on A. Second, A depended on the number of sampled sites n. With small and intermediate n, the true A¬ could not be recovered in any of the models. Third, A depended on the distance d between sampled sites. With small d, A was overestimated, while with large d, A was underestimated.
Since under subsampling, the observables depended on the model's topology and interaction mechanisms, we propose that systematic subsampling can be exploited to compare models with neural data: When changing the number and the distance between electrodes in neural tissue and sampled units in a model analogously, the observables in a correct model should behave the same as in the neural tissue. Thereby, incorrect models can easily be discarded. Thus, systematic subsampling offers a promising and unique approach to model selection, even if brain activity was far from being fully sampled.

The neuroanatomical connectivity of cortical circuits is believed to follow certain rules, the exact origins of which are still poorly understood. In particular, numerous nonrandom features, such as common neighbor clustering, overrepresentation of reciprocal connectivity, and overrepresentation of certain triadic graph motifs have been experimentally observed in cortical slice data. Some of these data, particularly regarding bidirectional connectivity are seemingly contradictory, and the reasons for this are unclear. Here we present a simple static geometric network model with distance-dependent connectivity on a realistic scale that naturally gives rise to certain elements of these observed behaviors, and may provide plausible explanations for some of the conflicting findings. Specifically, investigation of the model shows that experimentally measured nonrandom effects, especially bidirectional connectivity, may depend sensitively on experimental parameters such as slice thickness and sampling area, suggesting potential explanations for the seemingly conflicting experimental results.